Hybrid collective excitations in topological superconductor/ferromagnetic insulator heterostructures

We develop a linear response theory for the dynamical proximity effect in topological superconductor/ferromagnetic insulator (TS/FI) hybrids. Our approach integrates the nonequilibrium quasiclassical Keldysh-Usadel formalism for the TS with the Landau-Lifshitz-Gilbert equation for the FI's magnetization dynamics. This framework reveals a proximity-induced coupling between magnons and superconducting collective modes. Crucially, we find that spin-momentum locking in the TS surface state drives a hybridization between magnons and the superconducting Nambu-Goldstone (phase) mode, giving rise to composite magnon-Nambu-Goldstone excitations. We analyze the coupling strength's dependence on key parameters both analytically and numerically. In contrast, we demonstrate that the Higgs (amplitude) mode does not couple to magnons at linear order and is thus excluded from the hybrid excitation spectrum. The hybridization between magnons and the superconducting phase mode provides a mechanism for the interconversion of spin signals and the spinless signals carried by collective superconducting excitations, thereby giving new impetus to the development of superconducting spintronics.